7.6 Entropy Change in Irreversible Processes.
dU = Tds – PdV
where T and S, and -P and V are said to be canonically conjugate pairs.
where X and x, Y and y are by definition canonically conjugate pairs.
Then dM = dZ – Xdx – xdX –Ydy – ydY
dM = -xdX - ydY
dQ ≤ T∆S with dQ = ∆U + P ∆V
∆U + P ∆V ≤ T∆S
∆U + P ∆V - T∆S ≤ 0
(∆G)T,P≤ 0 at constant T and P
or G f ≤ Gi